Flying object

ABSTRACT

By using the interaction between the wind flow and the stabilizer arranged in the wind flow and along the direction of the wind flow, this invention provides the flying object that secures the stability of device or aircraft or stabilizer itself unified with the stabilizer by above effect. The interaction mentioned above is that when the wind flow hits the stabilizer at a certain angle, the wind flow changes the direction, and the power corresponding its reaction is given to the stabilizer by its reaction.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to flying objects and can be applied to theflying object with the propeller that can make stable vertical take off,landing, and hovering and to it's technology.

2. Description of the Background Technology

At present, there has been helicopters and similar aircrafts (ex. V-22combat plane of the United States Army that applies the tilt-rotorsystem) as the aircraft that can make VTOL (Vertical Take Off andLanding) and Hovering, besides F-35B, combat plane of the United StatesArmy, that applies variable nozzle which can change the angle of theirnozzle. All of these aircrafts need a very high level control techniqueand besides it is essential for these aircrafts to be controlled by highlevel sensor and high speed computer. For these reasons, body weightincreases much and production cost also increases very much, and then ithas been almost impossible to apply these technologies to regularairplanes.

Under this circumstance, if some good solution for above problems arefound now, we can expect a great progress for aviation field.

Incidentally, Japanese Published Unexamined Application No. 1992-5199,Japanese Published Unexamined Application No. 1994-293296, JapanesePublished Unexamined Application No. 2006-327219, Japanese PublishedUnexamined Application No. 2007-118891, Japanese Unexamined PatentApplication Publication No. 2005-533700, Japanese Unexamined PatentApplication Publication No. 2007-521174, Japanese Published UnexaminedApplication No. 1993-39092, and Japanese Published UnexaminedApplication No. 1995-232699, has already been published as the precedingtechnical document related to the background technology of thisinvention.

Above practical aircrafts developed so far, has had such problem thatthe instability became bigger by the wind flow which they generated bythemselves. Besides, because of such other unstable elements that thevibration of the body caused by the rotational vibration of the rotator(propeller), the staggering of the body caused by the side wind, tosecure the stability of the aircraft when the aircraft is makingvertical take off, landing and hovering, has still been a very seriousproblem until now.

SUMMARY OF THE INVENTION

The purpose of this invention is to provide flying objects withoutstanding stability by applying flying objects with propeller that canmake stable vertical take off and landing or stable hovering.

The flying object of the first aspect of this invention is that theradial stabilizing wing is arranged as the relationship between thevertical distance n_(GC) between the center point of total wind flowpressure obtained by synthesizing the center point of wind flow pressureof the respective stabilizing wings and the center of gravity of theconcerned flying object, and the vertical distance n_(GW) between thecenter point of outside wind pressure and the center of gravity of theflying object is represented by formula (26).

According to this aspect, the concerned flying object can hover stably.

The flying object of the second aspect of this invention is that theradial stabilizing wing is arranged as the relationship between thevertical distance n_(GC) between the center point of total wind flowpressure obtained by synthesizing the center point of wind flow pressureof the respective stabilizing wings and the center of gravity of theconcerned flying object, and the vertical distance n_(GW) between thecenter point of outside wind pressure and the center of gravity of theflying object is represented by formula (26).

According to this aspect, the concerned flying object can hover stably.

The flying object of the third aspect of this invention is that theradial stabilizing wing is arranged as the relationship between thevertical distance n_(GC) between the center point of total wind flowpressure obtained by synthesizing the center point of wind flow pressureof the respective stabilizing wings and the center of gravity of theconcerned flying object, and the vertical distance n_(GW) between thecenter point of outside wind pressure and the center of gravity of theflying object is represented by formula (26), besides, is arranged asthat the relation between minute part of each stabilizing wing and thecenter of gravity is represented by formula (28).

According to this aspect, the concerned flying object can hover stably.

The flying object of the fourth aspect of this invention is that theradial stabilizing wing is arranged as the relationship between thevertical distance n_(GC) between the center point of total wind flowpressure obtained by synthesizing the center point of wind flow pressureof the respective stabilizing wings and the center of gravity of theconcerned flying object, and the vertical distance n_(GW) between thecenter point of outside wind pressure and the center of gravity of theflying object is represented by formula (26), besides, is arranged asthat the relation between minute part of each stabilizing wing and thecenter of gravity is represented by formula (29).

According to this aspect, the concerned flying object can hover morestably.

The flying object of the fifth aspect of this invention is that thecylindrical stabilizing wing is arranged as the relationship between thevertical distance n_(GC) between the center point of total wind flowpressure obtained by synthesizing the center point of wind flow pressureof the respective stabilizing wings and the center of gravity of theconcerned flying object, and the vertical distance n_(GW) between thecenter point of outside wind pressure and the center of gravity of theflying object is represented by formula (26).

According to this aspect, the concerned flying object can hover stably.

The flying object of the sixth aspect of this invention is thatcylindrical stabilizing wing is arranged as the relationship between thevertical distance n_(GC) between the center point of total wind flowpressure obtained by synthesizing the center point of wind flow pressureof the respective stabilizing wings and the center of gravity of theconcerned flying object, and the vertical distance n_(GW) between thecenter point of outside wind pressure and the center of gravity of theflying object, is represented by formula (26), besides, is arranged asthat the relation between minute part of each stabilizing wing and thecenter of gravity is represented by formula (34).

According to this aspect, the concerned flying object can hover morestably.

The flying object of the seventh aspect of this invention is the flyingobject comprising the aircraft described in any one of claims 1 to 4 andthe aircraft described in any one of claim 5 or claim 6, and wherein therespective wind flow generating devices share one wind flow generatingdevice.

According to this aspect, the concerned aircraft can hover stably.

The flying object of the eighth aspect of this invention is the flyingobject comprising two or more of the same flying objects described inany one of claims 1 to 7, which are arranged at intervals with centralaxes thereof being parallel to each other and each has an upwardlydirected intake and a downwardly directed exhaust, and a connectingmember that connects said two or more of the same flying objects to eachother.

According to this aspect, the concerned flying object can hover morestably.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plane figure and side view of propeller aircraft 60A forexplaining propeller aircraft 60A (when multiple π effect works)concerning Embodiment 1.

FIG. 2 is a drawing which explains the Theory of New Lifting Power.

FIG. 3 is a drawing for explaining propeller aircraft 60B (when multipleπ effect does not work) concerning Embodiment 1.

FIG. 4 is a drawing which explains the condition to offset and stabilizethe influences caused by the vibration of the rotational axis of thepropeller.

FIG. 5 is a drawing which describes the situation that the propellerwind is flowing along the hem of the lower stabilizing wing.

FIG. 6 is a drawing which describes the method to stop the exceedingpropeller wind flowing along the hem of the lower stabilizing wing.

FIG. 7 is an example of perspective view of the aircraft which comprisescylindrical stabilizing wing and radial stabilizing wing.

FIG. 8 is a plane figure of the aircraft 80 in FIG. 7, which is forcalculating the wind pressure power that comes from the wind flow of theinside of the cylinder and that is applied to the inside wall of thecylindrical stabilizing wing.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

It has been cleared during many experiments that the source of thelifting power is the effect of action and reaction of wind flow againstthe wing. It has been succeeded to make clear the relationship betweenthe power that the propeller wind affects each stabilizing wing, and thewind pressure power by the air around the aircraft, by making smallaircrafts (a model, controllable by radio control) that have the deltawing drawn in FIG. 1 and FIG. 3 or the cylindrical stabilizing wing(duct wing) in FIG. 7, and by repeating hovering experiments by remotecontrolling with radio control.

FIG. 2 is the drawing that explains the theory of New Lifting Power, andis the cross sectional view VI-VI in FIG. 1 and FIG. 3. Here, supposethat aircraft 60A(60B) is holding the weight mg of the aircraft andhovering. F_(p) in FIG. 2 represents the thrust of propeller 60, β isthe angle of the vibration of the top-end of the rotational axis ofpropeller 60 a. And the mark a (=g tan β) represents the acceleration ofthe aircraft 60A(60B) that is going to start moving horizontally byslanting of the propeller thrust F_(p) at angle β, when the top of therotational axis of propeller 60 a vibrates at angle β.

The vibration of the rotational axis of propeller 60A is rotating in alldirections and the vertical element of thrust F_(p) is holding theweight of the aircraft 60A(60B). Consequently, the wind power that blowsdownward from propeller 60, flows down along stabilizing wing 61 ofaircraft 60A(60B) with the power of average mg. At this moment, theaircraft 60A(60B) begins to move horizontally at accelerate a. So, thewind that flows downward with power mg hits the stabilizing wing 61 ofaircraft 60A(60B) at angle β as FIG. 2.

At this moment, it is cleared that the power F_(p) sign β is applied tothe horizontal line located at any distance d from propeller 60 on thestabilizing wing(the part of stabilizing wing which is located inside ofdotted line that represents the spread of propeller wind that spreads atangle α from propeller 60 in FIG. 1 or 3) within the range wherepropeller wind is flowing. Let the wind pressure power from propellerwind towards entire stabilizing wing (called propeller wind pressurehereafter) be F_(c), according to the dynamics, F_(c) should be L F_(p)sin β, but it is getting cleared that the actual value of the powerF_(c) is represented by formula (1) or formula (2), by the analysis inhovering experiments with the aircraft in FIG. 1 and FIG. 3. Here, r₀represents the diameter of propeller 60, and n is multiple coefficientof height L of trapezoid wing arranged under propeller 60 of theaircraft in FIG. 1, for the diameter of propeller r₀. S_(C) representsthe area of the diagonal part in FIG. 1 or FIG. 3.

In the case of the aircraft in FIG. 1 (when the value of the L isrelatively small)

$\begin{matrix}{F_{C} = {{n\; \pi \; F_{P}\sin \; \beta} = {\frac{S_{C}}{r_{0}^{2}}\pi \; F_{P}\sin \; \beta}}} & (1)\end{matrix}$

In the case of the aircraft in FIG. 3 (when the value of L is relativelybig)

$\begin{matrix}{F_{C} = {\frac{S_{C}}{r_{0}^{2}}F_{P}\sin \; \beta}} & (2)\end{matrix}$

The difference between formula (1) and formula (2) is that whether ithas π or not.

In accordance with the height L of stabilizing wing underneath thepropeller, π coefficient appears or does not appear. As the result ofthe experiments in which the value of L is changed, the value ofmultiple coefficient n of L which is the boundary between appearing anddisappearing of π coefficient has some range, and when the value ofmultiple coefficient n of L is about 2.4 or less, it seems that πcoefficient appears. And also, when the value of multiple coefficient nof L is 3.0 or more, it seems that π coefficient disappears. Hereafterit is called multiple π effect when π coefficient is appearing, and itis called 1 multiple effect when π coefficient is not appearing.

And also here, the calculation of area S_(C) is to convert the area ofthe stabilizing wing inside of the propeller wind into the area ofstabilizing wing inside of propeller wind when the spreading propellerwind is shrunk into the condition that it does not spread at all (thecondition that propeller wind flows without changing the air densitydirectly under the propeller as parallel flow). But the way ofcalculation is different between the case of FIG. 1 (L is relativelysmall) and the case of FIG. 3 (L is relatively big). In the case of FIG.1, it is calculated as that the way of spreading of the propeller windon the stabilizing wing is only two dimensional spreading on thestabilizing wing, on the other hand, in the case of FIG. 3, it iscalculated as that the way of spreading of the propeller wind is threedimensional spreading. The concrete way of calculating is as follows.

Suppose horizontal line on the stabilizing wing located at the place anydistance d from propeller 60. When r_(w) represents the width of thespreading of the propeller wind on said horizontal line, and r_(a)represents the width of the stabilizing wing inside of propeller wind(in the case FIGS. 1 and 3, r_(w)=r_(a)), and also, r represents thewidth of the stabilizing wing on said horizontal line after theshrinking, the formula will be (3), (4).

In the case of the aircraft in FIG. 1 (when multiple π effect works) (inthe case of FIG. 1, r_(a)=r_(w))

$\begin{matrix}{r = {{r_{a}\left( \frac{r_{0}}{r_{w}} \right)} = r_{0}}} & (3)\end{matrix}$

In the case of the aircraft in FIG. 3 (when multiple π effect doesn'twork) (in the case of FIG. 3, r_(a)=r_(w))

$\begin{matrix}{r = {{r_{a}\left( \frac{r_{0}}{r_{w}} \right)}^{2} = \frac{r_{0}^{2}}{r_{w}}}} & (4)\end{matrix}$

As mentioned above, after drawing the shrinking drawing of thestabilizing wing inside of propeller wind, the center point of propellerwind pressure C_(p) should be obtained. When multiple π effect works,the center point of propeller wind pressure, as known before, appears atthe place removed below from the front end of the stabilizing wing ofsaid shrinking drawing of the stabilizing wing by ¼ length of the wingchord of concerned shrinking stabilizing wing. But, when multiple πeffect doesn't work, the existing theory of Lifting Power doesn't work,and normal center point of outside wind pressure for the stabilizingwing of said shrinking drawing of the stabilizing wing drawn by usingformula (4) which is considered that the air density is becoming thinneras the propeller wind spreads three dimensionally, becomes the centerpoint of propeller wind pressure.

Usually, under the condition that there is completely no stabilizingwing under the propeller, the spreading angle of propeller wind α willbe around 0.2-0.24, when it is represented by tan α. When the aircraftis like the one in FIG. 1 (the air craft that has relatively small L),tan α is around 0.08˜0.12, when the aircraft is like the one in FIG. 2(the aircraft that has relatively big L), it is confirmed by experimentsthat tan α is around 0.2˜0.24.

This phenomenon is considered as that when a stabilizing wing which hasrelatively small value of L is existing inside of the propeller wind,the spreading of propeller wind is controlled to some extent by Coandaeffect, as the value of L is becoming bigger, the spreading degree ofpropeller wind is becoming bigger, and when the spreading degree ofpropeller wind becomes bigger than a certain degree near the lower areaof stabilizing wing, the air density near the lower area of stabilizingwing becomes small and the air flow on the stabilizing wing will bepeeled off. Once this kind of peeling off condition happens at thelowest part of stabilizing wing, this peeling off condition seems toaffect to the top of the stabilizing wing.

Now, in FIG. 2, suppose the case that the top of rotational axis ofpropeller 60 a is slanting not in all directions but to only onedirection at angle β, and besides, suppose the case that aircraft 60A inFIG. 1 is flying horizontally, F_(p) in formula (1) is considered as thethrust to horizontal direction of said aircraft 60A, and angle β isconsidered as the angle that main wing 61 of concerned aircraft 60A isslanting to the direction of movement, that is to say an attack angle ofmain wing 61, then the formula (1) is surely considered as the Formulaof Lifting Power.

Regarding formula (2) related to the aircraft in FIG. 3, it is differentfrom the regular lifting power because the multiple π effect doesn'twork there, but it is the lifting power under the special circumstance.

In general, airplane with fixed wing gets the lifting power by movinghorizontally. It is considered that the condition that the fixed wing ofthis kind of airplane is moving horizontally in the air with attackangle, and the condition that the aircraft 60A in which stabilizing wing61 is arranged along the rotational axis of propeller 60 a is beginningto move horizontally by the vibration of the rotational axis ofpropeller 60 a during hovering, is totally same with regard to the powertowards each fixed wing of the airplane and stabilizing wing of aircraft60A. It is also considered that formula (1) is the formula whichrepresents the generally called as lifting power, by the thrust powerwhich is completely different element from old one, and by squaremultiple coefficient of diameter r₀ of propeller 60.

In the experiments of hovering with many kinds of aircrafts, theimportant condition for making the aircraft hovering stably wasdiscovered, besides above new theory of lifting power was established.This means that it is impossible to make stable hovering unless thecenter of gravity G is arranged at the point where line segment C_(p)Wis divided by calculating proportionally according to the size of eachwind pressure power towards the action center point of propeller windpressure power by the propeller wind onto the stabilizing wing arrangedunder the propeller of hovering aircraft (called center point ofpropeller wind pressure hereafter) C_(p), and towards the action centerpoint of regular wind pressure power from the side by the still airaround the aircraft (called center point of outside wind pressurehereafter) W.

Here, suppose the regular wind pressure power from the side by the stillair around the aircraft against propeller wind pressure power F_(c), isrepresented by F_(W). The relationship between Fc and F_(w) is obtainedby the experiments, and becomes formula (5), formula (6).

In the case of the aircraft in FIG. 1 (when the value of L is relativelysmall (when multiple π effect works))

$\begin{matrix}{F_{W} = {{\frac{W}{n\; \pi}F_{C}} = {{\frac{W}{\frac{S_{C}}{r_{0}^{2}}\pi}F_{C}} = {{WF}_{P}\sin \; \beta}}}} & (5)\end{matrix}$

In the case of the aircraft in FIG. 3 (when the value of L is relativelybig (when multiple π effect does not work))

$\begin{matrix}{F_{W} = {{\frac{W}{\frac{S_{C}}{r_{0}^{2}}}F_{C}} = {{WF}_{P}\sin \; \beta}}} & (6)\end{matrix}$

Here, W is represented by formula (7) when the projected area of theaircraft is represented by S_(w).

$\begin{matrix}{W = \frac{S_{W}}{S_{C}}} & (7)\end{matrix}$

Here again, when n_(GC) represents multiple coefficient of the verticaldistance between the center point of propeller wind pressure C_(p) andthe center of gravity G for the diameter of propeller r₀, and whenn_(GW) represents the multiple coefficient of vertical distance betweenthe center point of outside wind pressure W and G for the diameter r₀,the formula (8), and (9) are held.

$\begin{matrix}{{\frac{F_{C}}{F_{W}} = {\frac{n\; \pi}{W} = {\frac{\frac{S_{C}}{r_{0}^{2}}\pi}{W} = \frac{n_{GW}}{n_{GC}}}}}\left( {{when}\mspace{14mu} {multiple}\mspace{14mu} \pi \mspace{14mu} {effect}\mspace{14mu} {works}} \right)} & (8) \\{{\frac{F_{C}}{W_{W}} = {\frac{\frac{S_{C}}{r_{0}^{2}}}{W} = \frac{n_{GW}}{n_{GC}}}}\left( {{when}\mspace{14mu} {multiple}\mspace{14mu} \pi \mspace{14mu} {effect}\mspace{14mu} {doesn}^{\prime}t\mspace{14mu} {work}} \right)} & (9)\end{matrix}$

Here, let S_(C)/r₀ ²=H_(C), then formula (10) and (11) are held

H_(C) πn_(GC)=W n_(GW) (when multiple π effect works)   (10)

Or

H_(C) n_(GC)=W n_(GW) (when multiple π effect doesn't work)   (11)

Hereafter this H_(C) is called wind flow pressure coefficient. Theaircraft can make stable hovering if it is planned as formula (10),(11), the conditional formulas for stable hovering, are satisfied. Ofcourse, the calculated value of the position of the center of gravity onthe main wing viewed from the front of the aircraft has to becorresponded with the calculated value of the position of the center ofgravity on the side wing viewed from the side of the aircraft.

The unstable element of the hovering aircraft is not only that thepropeller wind pressure power F_(c) applied to said center point ofpropeller wind pressure Cp and the outside wind pressure power F_(W)applied to the center point of outside wind pressure F_(W), are notbalanced against the center of gravity, but also that there exist onemore big unstable element. As explained in FIG. 2, the rotational axisof the propeller always vibrates with a certain angle big or small, andthis vibration is rotating in all directions. This condition isunpreventable, because of this circumstance, the vibration of theaircraft is becoming bigger gradually, and finally it becomesuncontrollable.

The method to prevent the vibration of the aircraft caused by thevibration of rotational axis of propeller is to use each wind pressuremoment by propeller wind pressure power F_(C) applied to the aircraft,and outside wind pressure power F_(W), for the center of gravity G.

The FIG. 4 is for explaining how to arrange the center point ofpropeller wind pressure Cp and the center point of outside wind pressureW in order to prevent the vibration of the aircraft caused by thevibration of rotational axis of the propeller. Suppose propeller 81 andstabilizing wing 82 under it are arranged on aircraft 80 in FIG. 4, andnow the concerned aircraft is hovering with the condition that theweight of the aircraft mg and the vertical element of thrust power F_(P)of propeller 81 are balanced each other. FIG. 4 shows the moment whenthe rotational axis of propeller is slanting at angle β against thevertical line. At this moment, the aircraft is in condition that it isdrawn to the direction that propeller 81 is slanting with the powerF_(P) sin β, the aircraft starts rotating around the center of gravity Gof rotating center, but at this moment, propeller wind pressure powerF_(C) and outside wind pressure power F_(W) works as the moment ofopposite direction against the direction the aircraft is going torotate, and if the total moment of F_(C) and F_(W) is bigger than themoment of F_(P) sin β, the rotating of the aircraft stops. When thiscondition is represented by the moment balance formula it becomesformula (12). Provided the multiple coefficient of the vertical distancefrom the fixed point of rotational axis of propeller to the center ofgravity G for the diameter of propeller r₀ is n_(G), and the multiplecoefficient of the distance from the fixed point of rotational axis ofpropeller to the top of rotational axis of propeller for the diameter ofthe propeller r₀ is n_(a).

n _(GC) F _(C) +n _(GW) F _(W)+mgn_(a) sin β≧F _(P) sin β(n _(a) cos β+n_(G))   (12)

According to FIG. 2, F_(P)=mg/cos β, F_(C)=H_(C) π mg tan β, F_(W)=W mgtan β, so, put above formulas into formula (12), then formula (13),(14), are given.

H _(C) π n _(GC) +W n _(GW) ≧n _(G) (when multiple π effect works)  (13)

Or

H _(C) n _(GC) +W n _(GW) ≧n _(G) (when multiple π effect doesn't work)  (14)

As above, to hold formula (10), (11), (13), (14), is the conditionneeded for the aircraft to make stable hovering. However, formula (13),(14) are not precise. It is simplified for explaining simply the methodto prevent the vibration of the aircraft from the vibration ofrotational axis of propeller.

Actually, there has been many aircrafts with condition n_(GC)=n_(GW)=0,in other words, even the aircraft, which is planned as the center pointof propeller wind pressure C_(p), the center point of outside windpressure W, and the center of gravity G are corresponded each other, canmake stable hovering. The value of n_(G) of these aircraft are enoughbigger than 0, and H_(C) n_(GC)+W n_(GW) is of course 0. This shows thatformula (13), (14) is not held.

As above, the reason why the aircraft with condition n_(GC)=n_(GW)=0 canmake stable hovering is that the calculation of moment by the windpressure around the center of gravity should not be calculated only bythe distance between the center point of wind pressure and the center ofgravity, it should be calculated as the total sum of minute momentaround the center of gravity brought by the wind pressure of all theminute part of the wing like the calculation of the moment of inertia.Considering this circumstance and rewrite formula (13), (14), theybecome formula (15), (16). Provided, let the area of each minute part ofthe stabilizing wing after shrinking inside of the propeller wind beS_(ci), the area of each minute part of projection area of the aircraftbe S_(wk), and each multiple coefficient of the vertical distancebetween each minute part and the center of gravity G of the aircraft forthe diameter of the propeller r₀ be n_(GCi), n_(GWk), furthermore, letH_(ci)=S_(ci)/r₀ ².

$\begin{matrix}{{{{\pi \; {\sum\limits_{i}{H_{C\; i}n_{GCi}}}} + {\frac{W}{S_{W}}{\sum\limits_{k}{S_{Wk}n_{GWk}}}}} \geq {n_{G}\left( {{when}\mspace{14mu} {multiple}\mspace{14mu} \pi \mspace{14mu} {effect}\mspace{14mu} {works}} \right)}}{Or}} & (15) \\{{{\sum\limits_{i}{H_{Ci}n_{GCi}}} + {\frac{W}{S_{W}}{\sum\limits_{k}{S_{Wk}n_{GWk}}}}} \geq {n_{G}\left( {{when}\mspace{14mu} {multiple}\mspace{14mu} \pi \mspace{14mu} {effect}\mspace{14mu} {doesn}^{\prime}t\mspace{14mu} {work}} \right)}} & (16)\end{matrix}$

As mentioned above, it is clear that the basic condition of stablehovering of the aircraft is to let formula (10), (11), and formula (15),(16) be satisfied.

The first reason of making the hovering aircraft unstable was becausethe center point of propeller wind pressure C_(p) did not correspondwith the center point of outside wind pressure W, and the second reasonwas because of the vibration of the rotational axis of the propeller. Itis clear that the method of preventing the vibration of the aircraftcaused by each reason is to plan the aircraft to satisfy the formula(10), (11), and the formula (15), (16). But it is also very important toconsider that the flow of the air shows unexpected move by Coandaeffect, and the effect to the aircraft by the flow of the air around thepropeller besides the propeller wind.

FIG. 5 shows the flow of propeller wind flows out along the hem of lowerpart of stabilizing wing towards the outside of the spread of regularpropeller wind by Coanda effect. In this kind of case, it is impossibleto get correct result by calculating the position of the center ofgravity with the basic calculation mentioned before.

In the case of basic calculation, for example, in the case of FIG. 1since the calculation of the area of the stabilizing wing inside of thepropeller wind S_(C) is calculated with the image that the real shape ofstabilizing wing existing in the actual propeller wind shrinks at thesame time when the spreading angle α of propeller wind shrinks into 0,as a result, the shape of the stabilizing wing in the spreadingpropeller wind becomes rectangle with width r₀ after calculation ofshrinking. The area of this rectangle becomes Sc. And also the centerpoint of propeller wind pressure of this rectangle stabilizing wingbecomes the actual center point of propeller wind pressure of theaircraft C_(p). But in the case of FIG. 5, since there is some exceedingflow from the normal flow, so the shape of the stabilizing wing of thisexceeding flow part has to be shrunk by the same calculating formula.The diagonal part in FIG. 5 is the shape after the shrink calculation ofthe stabilizing wing inside of the spreading propeller wind by the basiccalculation. The shape of its exceeding part of stabilizing wing afterthe shrink calculation is the shaded part in FIG. 5. Hence the valuegiven by the addition of the area of stabilizing wing S_(C) inside ofshrinking propeller wind after the basic shrink calculation to the areaof this shadow Sa should be the total area of stabilizing wing aftershrinking. When this total area of stabilizing wing after shrinking isrepresented by [S_(C)], then formula (17) is given.

[S _(C) ]=S _(C) +S _(a)   (17)

The method to prevent the exceeding of propeller wind is shown in FIG.6. As FIG. 6, it is to arrange the stopper at the middle of the hem ofthe stabilizing wing along which the exceeding wind is flowing. In theactual experiment, it was done with the aircraft 50 like the one in FIG.5, the exceeding wind was blocked completely by placing this stopper,consequently the anti-torque offsetting power of whole aircraftdecreased and aircraft 50 started rotating into reverse. The centerpoint of total wind flow pressure of whole aircraft 50 at that timemoved upper than before placing the stopper, so it went without sayingthat the center of gravity to balance the aircraft also moved up.

In FIG. (1), (3), (5), regarding aircraft 60(A), 60(B), the triangleupper stabilizing wing is arranged above propeller 60, and the upperpart stabilizing wing like the shape of Kabuto (Japanese helmet forsamurai) is arranged around propeller 51 of the aircraft 50. These upperstabilizing wings were arranged to improve the stability of the aircraftduring hovering, but at the beginning of the experiment, it was meantonly to adjust the position of center point of outside wind pressure W.In repeating many experiments, it was becoming cleared that thesestabilizing wings received the wind pressure more than outside windpressure. Also it was becoming cleared that there was some delicateposition gap between the calculated value of the position of the centerof gravity that makes the aircraft stable and actual stabilizingposition of the center of gravity, and according to the calculation withthe size of the distance of the position gap, not only the outside windpressure but also 1/π times the wind pressure by some wind flow wereapplied to these upper stabilizing wings (comparative multiple whenmultiple π effect does not work and the propeller wind pressure iscalculated as 1 time). And it was becoming cleared that the calculationof the center point of wind flow pressure by the wind flow of only theseupper stabilizing wing was done by common calculation method of thecenter point of outside wind pressure.

The size of wind flow pressure of 1/π applying to the upper stabilizingwing except these outside wind pressure can be expressed as formula (18)if the size is represented by F₀. Provided let S₀ be actual area ofupper stabilizing wing.

$\begin{matrix}{F_{0} = {\frac{1}{\pi}\left( \frac{S_{0}}{r_{0}^{2}} \right)F_{P}\sin \; \beta}} & (18)\end{matrix}$

It can be easily confirmed that there is air flow on the propellerabsorbed into propeller (called front air flow of propeller hereafter).It is clear that this absorbed air flow generates the wind pressure of1/π as mentioned above. This kind of front air flow of propeller seemsto spread around the propeller (including the below part from propeller)except the space where propeller wind is flowing, in some range (therange about 2 to 4 times of diameter of the propeller from the centerpoint of rotation of propeller).

Now, let formula (19), (20) be as below, besides total wind flowpressure coefficient is represented by [H], formula (21), (22) areexpressed as below.

$\begin{matrix}{H_{a} = \frac{S_{a}}{r_{0}^{2}}} & (19) \\{H_{0} = \frac{S_{0}}{r_{0}^{2}}} & (20) \\{{\lbrack H\rbrack = {{\pi \left( {H_{C} + H_{a}} \right)} + {\frac{1}{\pi}{H_{0}\left( {{when}\mspace{14mu} {multiple}\mspace{14mu} \pi \mspace{14mu} {effect}\mspace{14mu} {works}} \right)}}}}{Or}} & (21) \\{\lbrack H\rbrack = {H_{C} + H_{a} + {\frac{1}{\pi}{H_{0}\left( {{when}\mspace{14mu} {multiple}\mspace{14mu} \pi \mspace{14mu} {effect}\mspace{14mu} {does}\mspace{14mu} {not}\mspace{14mu} {work}} \right)}}}} & (22)\end{matrix}$

Also, when the value obtained by converting the area of the upperstabilizing wing S₀ into the shrunk area of the stabilizing wing insideof propeller wind, is added to the total area of stabilizing wing aftershrinking [S_(C)], formula (17) becomes formula (23), (24).

$\begin{matrix}{{\left\lbrack S_{C} \right\rbrack = {S_{C} + S_{a} + {\frac{1}{\pi^{2}}{S_{0}\left( {{when}\mspace{14mu} {multiple}\mspace{14mu} \pi \mspace{14mu} {effect}\mspace{14mu} {works}} \right)}}}}{Or}} & (23) \\{\left\lbrack S_{C} \right\rbrack = {S_{C} + S_{a} + {\frac{1}{\pi}{S_{0}\left( {{when}\mspace{14mu} {multiple}\mspace{14mu} \pi \mspace{14mu} {effect}\mspace{14mu} {does}\mspace{14mu} {not}\mspace{14mu} {work}} \right)}}}} & (24)\end{matrix}$

Hence, when the multiple coefficient of the projection area of theentire aircraft S_(W) which is receiving the outside wind pressure, forthe total area of stabilizing wing inside of propeller wind [S_(C)], isrepresented by [W], [W] becomes formula (25).

$\begin{matrix}{\lbrack W\rbrack = \frac{S_{W}}{\left\lbrack S_{C} \right\rbrack}} & (25)\end{matrix}$

As above, the formula of stable hovering condition of the aircraft whichcomprehends the exceeding of the propeller wind and the phenomenon ofsaid front air flow of propeller, is as follows.

Formula (10), (11) becomes formula (26).

[H]n_(GC)=[W]n_(GW)   (26)

Formula (13), (14) becomes formula (27).

[H]n _(GC) +[W]n _(GW) ≧n _(G)   (₂₇)

Formula (15), (16) becomes formula (28), (29).

$\begin{matrix}{{{{\pi \; {\sum\limits_{i}{H_{C\; i}n_{GCi}}}} + {\pi \; {\sum\limits_{j}{H_{aj}n_{Gaj}}}} + {\frac{1}{\pi}{\sum\limits_{m}{H_{0m}n_{G\; 0m}}}} + {\frac{\lbrack W\rbrack}{S_{W}}{\sum\limits_{k}{S_{Wk}n_{GWk}}}}} \geq {n_{G}\mspace{20mu}\left( {{when}\mspace{14mu} {multiple}\mspace{14mu} \pi \mspace{14mu} {effect}\mspace{14mu} {works}} \right)}}\mspace{20mu} {Or}} & (28) \\{{{\sum\limits_{i}{H_{Ci}n_{GCi}}} + {\sum\limits_{j}{H_{aj}n_{Gaj}}} + {\frac{1}{\pi}{\sum\limits_{m}{H_{0m}n_{G\; 0m}}}} + {\frac{\lbrack W\rbrack}{S_{W}}{\sum\limits_{k}{S_{Wk}n_{GWk}}}}} \geq {n_{G}\mspace{20mu}\left( {{when}\mspace{14mu} {multiple}\mspace{14mu} \pi \mspace{14mu} {effect}\mspace{14mu} {does}\mspace{14mu} {not}\mspace{14mu} {work}} \right)}} & (29)\end{matrix}$

Provided that the area of each minute part of the stabilizing winginside of the exceeding propeller wind after shrinking is represented byS_(aj), the area of each minute part of upper stabilizing wing byS_(0m), and the multiple coefficients of the vertical distances betweeneach minute part and the center of gravity for the diameter of propellerr₀, are represented as n_(Gaj), n_(G0m). And also let H_(aj)=S_(aj)/r₀ ₂, H_(0m)=S_(0m)/r₀ ₂ .

It can be considered that the total condition formula for the actualaircraft to make hovering stably is formula (26), (28) and (29). In thecase of hovering of actual aircraft, there may be air flows that areover our consideration yet, but since the most basic relational formula(5),(6),(7) between propeller wind pressure Fc and outside wind pressureF_(W) is universal and fundamental natural law, even if the aircraftreceives unexpected wind pressure power by special air flow, as long asthe size of this kind of power is confirmed by experiment, the positionof center of gravity for making the aircraft hovering stably by usingformula (26),(28) and (29) can be calculated and be given so soon.

Description of Embodiment 1

In this Embodiment 1, we planned and made the propeller aircraft 60Awith delta wing where multiple π effect is working as in FIG. 1, as tosatisfy formula (26),(27), and we put the center of gravity of theaircraft at the calculated position, and made it hovering. The resultwas that this aircraft showed very stable hovering.

Propeller aircraft 60A in this Embodiment is, as FIG. 1, mainlycomprised of the body 61 which has 2 vertical main wings 61 a that areassembled as radial and parallel, and propeller 60 which is arranged onthe top end of the body 61. Each main wing 61 a is formed each other asplate-shape and as half trapezoid-shape with same shape and size, andthe entire body of body 61 is formed as trapezoid and plate-shape(thatis Delta wing). The inclination angle α of the dotted line drawn asinclined in each main wing is the adjusted angle with the spread of thewind (propeller wind) from propeller 60 during hovering.

Furthermore, the mark L in FIG. 1 is the length of the body 61, mark r₀is the diameter of the propeller, mark d represents any distance belowpropeller 60, mark r_(a), r_(w) is the breadth of the stabilizing wingon the horizontal line located at distance d below propeller 60 insideof propeller wind and the breadth of the spreading of propeller wind,and in this case r_(a)=r_(W). The mark r is also the breadth of thestabilizing wing located on the horizontal line at a distance d belowpropeller 60 inside of the propeller wind after shrinking. And point C,C_(p), C_(o), W, G represents each center point of total wind flowpressure of the aircraft, the center point of propeller wind pressure,the center point of wind pressure of front air flow of propeller, thecenter point of outside wind pressure, and the point of the center ofgravity of the aircraft. Mark ρ_(o), and ρ_(d) is each the air densitydirectly under the propeller 60 and the air density at a distance dbelow propeller 60.

In FIG. 1, since multiple π effect is assumed to be working, the airdensity by the propeller wind ρ is inverse proportion against spreadwidth of propeller wind r_(W) Hence, the air density ρ_(d) at anydistance of d below the propeller wind is represented asρ_(d)=ρ_(o)(r₀/r_(w)). Then, suppose the width of the stabilizing wingis represented by r when the width of the stabilizing wing inside of thepropeller wind r_(a) is compressed from ρ_(d) to ρ_(o), then ρ_(d)r_(a)=ρ_(o) r is held. And in the case of aircraft 60A in FIG. 1,r_(a)=r_(w) is held and formula (3) is given.

$\begin{matrix}{r = {{r_{a}\left( \frac{r_{0}}{r_{w}} \right)} = r_{0}}} & (3)\end{matrix}$

The diagonal part of aircraft 60A in FIG. 1 is the shape of the shrunkstabilizing wing inside of the propeller wind obtained from formula (3).Then we obtain the area of this shrunk stabilizing wing Sc and thecenter point of the propeller wind pressure C_(p), furthermore, the areaof the entire aircraft S_(W) and the center point of outside windpressure W. Besides that, we obtain the area of upper stabilizing wingabove propeller S₀ and center point of front wind pressure of propellerC₀, then, since the upper stabilizing wing above the propeller isreceiving the wind pressure power of 1/π, in order to add said area S₀to the area of stabilizing wing inside of shrunk propeller wind whichhas multi π effect, we convert as (1/π²)S₀=S′₀, then the point whereline segment C_(P)C₀ is divided by calculating proportionally accordingto the area ratio between said converted area S′₀ and the area ofstabilizing wing after shrinking Sc, is the center point of total windflow pressure C. Finally the center of gravity G is arranged as formula(26) is satisfied. This aircraft itself controls the attitude naturallyagainst the rolling during hovering, then the pilot only controls therotations of propeller.

Description of Embodiment 2

Here we study how we should do to apply said conditional formula forstabilizing (26), (28) and formula (29) into the aircraft with multiplestabilizing wings, composed of cross stabilizing wing and cylindricalstabilizing wing in FIG. 7.

The aircraft 80 in FIG. 7 comprises propeller 81, and the stabilizingwing which is arranged under propeller 81 and which is rectangle shapeviewed from the side, for example the cross shape radial stabilizingwing of lower part 82, and cylindrical stabilizing wing 83 which isarranged as surrounding the radial stabilizing wing of lower part 82 andpropeller 81 on the coaxial line, and its lower end is extended at thesame height as the radial stabilizing wing of lower part 82 and its topend is extended upper side than propeller 81, and driving part (notdrawn) arranged at the radial stabilizing wing of lower part 82.

When cylindrical stabilizing wing 83 is arranged like aircraft 80, sincethe propeller wind is not spread, multiple π effect is working. Also itis clear that the air flow inside of the cylinder is parallel flow, andthe center point of wind flow pressure h of the inside wall of thecylindrical stabilizing wing 83 for the wind flow inside of cylinderappears at the point removed below from the top end of the cylindricalstabilizing wing 83 by ¼ length h₀ r₀ of the cylindrical stabilizingwing 83. r₀ is diameter of propeller. Also the center point of wind flowpressure C_(p) of the lower cross stabilizing wing 82 for the wind flowinside of cylinder appears at the point removed below from the top endof the lower cross stabilizing wing 82 by ¼ height n r₀ of the lowercross stabilizing wing 82. And then, the point obtained by dividingproportionally the segment line hC_(p) according to the ratio of thesize of two wind pressure powers that appear at these two center pointof wind flow pressures, is the center point of total wind flow pressureC. Point W is the center point of outside wind pressure, and the centerof gravity G for the aircraft 80 to make stable hovering is the pointobtained by dividing proportionally the segment line CW as formula (26)is satisfied.

Now, we study how much size of propeller wind pressure is applied to theinside wall of the cylindrical stabilizing wing 83.

FIG. 8 is the view of aircraft 80 from upper side (driving parts such aspropeller are not drawn). But the diameter of the circle is the lengthgiven by shrinking the inside diameter of the cylindrical stabilizingwing into propeller diameter r₀. Now, suppose that aircraft 80 begins tomove at acceleration a to downside in FIG. 8. At this moment let thewind pressure power that per unit area of the cross stabilizing wing 82receives from the wind flow of inside of cylinder be ΔF_(C1), the powerthat the inside wall of the cylinder at point B which advancedcounterclockwise at any angle (π/2)−α along the circumference from pointA which is on the cross stabilizing wing 82 in FIG. 8, is receivingvertically on its inside wall, becomes ΔF_(C2)=ΔF_(C1) cos α accordingto FIG. 8, and the vertical element of ΔF_(C2) becomes ΔF_(C3)=ΔF_(C1)cos² α. And when this ΔF_(C1) cos² α is integrated along thecircumference of inside cylinder in FIG. 8, it becomes total windpressure power ΔF_(C) _(φ) that circumference of inside wall of thecylinder is receiving from the wind flow of inside cylinder, the size ofit is formula (30).

$\begin{matrix}{{\Delta \; F_{C\; \varphi}} = {\frac{\pi}{2}r_{0}\Delta \; F_{C\; 1}}} & (30)\end{matrix}$

It becomes clear, according to formula (30), that the wind pressurepower F_(C) _(φ) that inside wall of cylindrical stabilizing wing isreceiving from the inside flow of the cylinder, is π/2 of the windpressure power F_(C) that one piece of flat plate stabilizing wing (theflat plate stabilizing wing that is the same shape and size as theshadow of the inside wall of the cylindrical stabilizing wing when it isprojected) which is the same width as inside diameter of cylindricalstabilizing wing and is the same length as cylindrical stabilizing wing,is receiving from the wind flow of inside of cylinder

$\begin{matrix}{F_{C\; \varphi} = {{\frac{\pi}{2}F_{C}} = {{H_{C}\left( \frac{\pi^{2}}{2} \right)}F_{P}\sin \; \beta}}} & (31)\end{matrix}$

We calculated the wind pressure power from the wind flow of inside ofthe cylinder to the cylindrical stabilizing wing in FIG. 8, followingthe formula (31), and obtained the center point of total wind flowpressure C of entire aircraft 80, and obtained the point between point Cand the center point of outside wind pressure W that satisfied theformula (26), and put the center of gravity on the point and made theaircraft 80 hovering. The aircraft 80 could make very stable hoveringlike the aircraft 60A in FIG. 1. Of course at that time, it went withoutsaying that the aircraft itself could control the attitude naturallyagainst the swaying in all directions, and the pilot did only thecontrol of propeller revolution.

The aircraft 80 comprises cross stabilizing wing. Since this crossstabilizing wing was needed for installing the driving part of propellerand for installing the cylindrical stabilizing wing as accurately aspossible, it became such aircraft with multiple stabilizing wingcomposed of cross stabilizing wing and cylindrical stabilizing wing asin FIG. 7. The purpose of the experiment was to obtain how much windpressure the propeller wind gave towards cylindrical stabilizing wing.As a result, the purpose of the experiment was achieved, and in the casethat the aircraft which comprises only cylindrical stabilizing wing, theconditional formula for stabilizing hovering, formula (26), formula (28)are given as below. The formula (26) is as below.

[H]n_(GC)=[W]n_(GW)   (26)

Provided

$\begin{matrix}{{\lbrack H\rbrack = {\frac{\pi^{2}}{2}H_{D}}}\;} & (32) \\{\lbrack W\rbrack = \frac{S_{W}}{\left\lbrack S_{C} \right\rbrack}} & (25) \\{\left\lbrack S_{C} \right\rbrack = {\frac{\pi}{2}S_{D}}} & (33)\end{matrix}$

Let H_(D)=S_(D)/r₀ ², and also let S_(D) be projection area of insidewall when inside diameter of cylindrical stabilizing wing is shrunk intodiameter of propeller r₀.

Formula (28) becomes formula (34).

$\begin{matrix}{{{\frac{\pi^{2}}{2}{\sum\limits_{q}{H_{D\; q}n_{GDq}}}} + {\frac{\lbrack W\rbrack}{S_{W}}{\sum\limits_{k}{S_{W,k}n_{GWk}}}}} \geq n_{G}} & (34)\end{matrix}$

Provided

$\begin{matrix}{\lbrack W\rbrack = \frac{S_{W}}{\left\lbrack S_{C} \right\rbrack}} & (25) \\{\left\lbrack S_{C} \right\rbrack = {\frac{\pi}{2}S_{D}}} & (33)\end{matrix}$

Let H_(Dq)=S_(Dq)/r₀ ², and let S_(Wk) be the area of each minute partof projection area S_(W) of entire aircraft, let S_(Dq) be the area ofeach minute part of said S_(D), and let n_(Gdq), n_(GWk) be multiplecoefficient of the vertical distance between each minute part that hasthe area of said each S_(Dq), S_(Wk) and the center of gravity of theaircraft for the diameter of propeller r₀.

Incidentally, for said aircraft with multiple stabilizing wing in FIG.7, since multiple π effect is working, said conditional formula (26) andformula (28) becomes as follows.

[H]n_(GC)=[W]n_(GW)   (26)

Provided

$\begin{matrix}{\lbrack H\rbrack = {{\pi \left( {H_{C} + H_{a}} \right)} + {\frac{1}{\pi}H_{0}} + {\frac{\pi^{2}}{2}H_{D}}}} & (35) \\{\lbrack W\rbrack = \frac{S_{W}}{\left\lbrack S_{C} \right\rbrack}} & (25) \\{\left\lbrack S_{C} \right\rbrack = {S_{C} + S_{a} + {\frac{1}{\pi^{2}}S_{0}} + {\frac{\pi}{2}S_{D}}}} & (36) \\{H_{D} = \frac{S_{D}}{r_{0}^{2}}} & (37)\end{matrix}$

(And in the case of FIG. 7, H_(a)=H₀=S_(a)=S₀=0)

$\begin{matrix}{{{\pi \; {\sum\limits_{i}{H_{Ci}n_{GCi}}}} + {\pi {\sum\limits_{j}{H_{aj}n_{Gaj}}}} + {\frac{1}{\pi}{\sum\limits_{m}{H_{0m}n_{G\; 0m}}}} + {\frac{\pi^{2}}{2}{\sum\limits_{q}{H_{D\; q}n_{GDq}}}} + {\frac{\lbrack W\rbrack}{S_{W}}{\sum\limits_{k}{W_{Wk}n_{GWk}}}}} \geq n_{G}} & (38)\end{matrix}$

Provided

$\begin{matrix}{\lbrack W\rbrack = \frac{S_{W}}{\left\lbrack S_{C} \right\rbrack}} & (25) \\{\left\lbrack S_{C} \right\rbrack = {S_{C} + S_{a} + {\frac{1}{\pi^{2}}S_{0}} + {\frac{\pi}{2}S_{D}}}} & (36) \\{H_{Dq} = \frac{S_{Dq}}{r_{o}^{2}}} & (39)\end{matrix}$

(And in the case of FIG. 7, H_(qj)=H_(0m)=S_(a)=S₀=0)

As we see formula (35), (36), (38), the section related to cylindricalstabilizing wing is simply added to each conditional formula of radialstabilizing wing (21), (23), (28). Although the form of formula (26)does not change in all condition, only the value of the marks [H], [W],[S_(C)], change according to the shape, condition of the aircraft asmentioned before.

In Description of Embodiment 1, the example of practicing of radialstabilizing wing was shown, in this Embodiment 2, the example ofpracticing of multiple stabilizing wing composed of radial stabilizingwing and cylindrical stabilizing wing was shown, and at the same timethe example of cylindrical stabilizing wing alone was shown. In actualscene, it seems that said multiple stabilizing wing will be often usedfor increasing the stability of the aircraft.

In contrast with that there are 2 kinds of conditions due to thecondition that multiple π effect works or does not work on the radialstabilizing wing as mentioned before, usually, multiple π effect alwaysworks in the cylindrical stabilizing wing whatever high the height ofthe cylindrical stabilizing wing may be. By combining these 2 kinds ofstabilizing wings, it becomes possible to create the aircraft that canmake more stable hovering.

The conditional formula for stable hovering of the aircraft composed ofthese 2 stabilizing wings, when multiple π effect is working on bothstabilizing wings, was described by [formula (26), formula (35), formula(25), formula (36), formula (37)], [formula (38), formula (25), formula(36), formula 39)], but when multiple π effect works only on cylindricalstabilizing wing, as described in the postscript of said [formula (26),formula (35), formula (25), formula (36), formula (37)], [formula (38),formula (25), formula (36), formula (39)], the form of formula (26) didnot change, and was simply to add the section related to cylindricalstabilizing wing to formula (22), formula (24), formula (29). Forreference, these formulas are listed below.

[H]n_(GC)=[W]n_(GW)   (26)

Provided

$\begin{matrix}{\mspace{79mu} {\lbrack H\rbrack = {H_{C} + H_{a} + {\frac{1}{\pi}H_{0}} + {\frac{\pi^{2}}{2}H_{D}}}}} & (40) \\{\mspace{79mu} {\lbrack W\rbrack = \frac{S_{W}}{\left\lbrack S_{C} \right\rbrack}}} & (25) \\{\mspace{79mu} {\left\lbrack S_{C} \right\rbrack = {S_{C} + S_{a} + {\frac{1}{\pi}S_{0}} + {\frac{\pi^{2}}{2}S_{D}}}}} & (41) \\{\mspace{79mu} {H_{D} = \frac{S_{D}}{r_{0}^{2}}}} & (37) \\{{{\sum\limits_{i}\; {H_{Ci}n_{GCi}}} + {\sum\limits_{j}\; {H_{aj}n_{Gaj}}} + {\frac{1}{\pi}{\sum\limits_{m}\; {H_{0m}n_{G\; 0m}}}} + {\frac{\pi^{2}}{2}{\sum\limits_{q}\; {H_{Dq}n_{GDq}}}} + {\frac{\lbrack W\rbrack}{S_{W}}{\sum\limits_{k}\; {S_{Wk}n_{GWk}}}}} \geq n_{G}} & (42)\end{matrix}$

Provided

$\begin{matrix}{\lbrack W\rbrack = \frac{S_{W}}{\left\lbrack S_{C} \right\rbrack}} & (25) \\{\left\lbrack S_{C} \right\rbrack = {S_{C} + S_{a} + {\frac{1}{\pi}S_{0}} + {\frac{\pi^{2}}{2}S_{D}}}} & (41) \\{H_{Dq} = \frac{S_{Dq}}{r_{o}^{2}}} & (39)\end{matrix}$

As above, two kinds of Embodiments, Embodiment 1 and Embodiment 2, weredescribed, but this invention should not be limited within these twokinds of Embodiments.

For example, such connected aircrafts comprising two or more of the sameaircrafts in any one of Embodiment 1 or Embodiment 2, which are arrangedat intervals with center axes thereof being parallel to each other, andeach has upwardly directed intake, and besides each aircraft isconnected to each other with the connecting member like a stick at alevel to ignore the projection area for example, are also included inEmbodiments.

The most basic matter for the aircraft to make stable hovering is toarrange the center of gravity of the aircraft under the thrust workingpoint, and besides, as in FIG. 1, FIG. 7, to put the center of gravityG, the center point of total wind flow pressure C, and the center pointof outside wind pressure W, on the center line of the aircraft on thestraight. If this is considered, the structure of said connectedaircraft needs to be the structure wherein each aircraft can make stablehovering alone, and besides wherein the multiple and completely sameaircrafts as above are connected. By making this structure, it can bepossible to place the total center of gravity G of the entire saidconnected aircraft, the center point of total wind flow pressure C, andthe center point of total outside wind pressure W, on the total centerline of the aircraft on the straight. Suppose the whole of saidconnected aircraft is as one aircraft, of course, formula (26) andformula (28), or formula (29), or formula (34), or formula (38) holds.

The experiment related to said connected aircraft was proceeded byconnecting 2 aircrafts 80 in FIG. 7. We designed the aircraft as formula(26) and formula (38) were held, put the center of gravity of theaircraft at the designed place, and when we made the connected aircrafthovering, the aircraft showed excellent stable hovering.

1. A flying object, comprising a wind flow generating device; and one ormore radial stabilizing wings arranged along the center axis of the windflow in the form of the coaxial line in the wind flow generated by thewind flow generating device, wherein said radial stabilizing wings arearranged such that the relationship between the vertical distance n_(GC)between the center point of total wind flow pressure obtained bysynthesizing the center point of wind flow pressure of the respectivestabilizing wings and the center of gravity of the flying object, andthe vertical distance now between the center point of outside windpressure and the center of gravity of the flying object, is representedby formula (26).[H]n_(GC)=[W]n_(GW)   (26) providing that: $\begin{matrix}{\lbrack H\rbrack = {{\pi \left( {H_{C} + H_{a}} \right)} + {\frac{1}{\pi}H_{0}}}} & (21) \\{\lbrack W\rbrack = \frac{S_{W}}{\left\lbrack S_{C} \right\rbrack}} & (25) \\{\left\lbrack S_{C} \right\rbrack = {S_{C} + S_{a} + {\frac{1}{\pi}S_{0}}}} & (23) \\{{H_{C} = \frac{S_{C}}{r_{0}^{2}}},{H_{a} = \frac{S_{a}}{r_{0}^{2}}},{H_{0} = \frac{S_{0}}{r_{0}^{2}}}} & (43)\end{matrix}$ where; r₀: a diameter of propeller S_(C): an area obtainedby converting the area of stabilizing wing inside of the spreadingpropeller wind into the area of stabilizing wing inside of the shrunkpropeller wind, when the spreading propeller wind is shrunk such thatthe propeller wind flows as a parallel wind flow without changing theair density directly under propeller, but its calculation of shrinkingrate is as follows. Suppose the horizontal line on the stabilizing winglocated at any distance from the propeller, and let the width ofspreading of the propeller wind on its horizontal line be r_(W), thewidth of the stabilizing wing inside of the propeller wind be r_(a), andalso the width of the stabilizing wing on its horizontal line aftershrinking be r, then r is represented by formula (3). $\begin{matrix}{r = {r_{a}\left( \frac{r_{0}}{r_{w}} \right)}} & (3)\end{matrix}$ S_(a): the area of stabilizing wing inside of exceedingpart of shrunk propeller wind when the area of stabilizing wing insideof the exceeding propeller wind from inside of said spreading propellerwind is shrunk at the shrinking rate represented by formula (3) S₀: thearea (except the area where propeller wind is flowing) of stabilizingwing of propeller periphery. S_(W): the projection area of the wholeaircraft.
 2. A flying object, comprising: a wind flow generating device;and one or more radial stabilizing wings arranged along the center axisof the wind flow in the form of the coaxial line in the wind flowgenerated by the wind flow generating device, wherein said radialstabilizing wings are arranged such that the relationship between thevertical distance n_(GC) between the center point of total wind flowpressure obtained by synthesizing the center point of wind flow pressureof the respective stabilizing wings and the center of gravity of theflying object, and the vertical distance n_(GW) between the center pointof outside wind pressure and the center of gravity of the flying object,is represented by formula (26).[H]n_(GC)=[W]n_(GW)   (26) Providing that: $\begin{matrix}{\lbrack H\rbrack = {\left( {H_{C} + H_{a}} \right) + {\frac{1}{\pi}H_{0}}}} & (22) \\{\lbrack W\rbrack = \frac{S_{W}}{\left\lbrack S_{C} \right\rbrack}} & (25) \\{\left\lbrack S_{C} \right\rbrack = {S_{C} + S_{a} + {\frac{1}{\pi}S_{0}}}} & (24) \\{{H_{C} = \frac{S_{C}}{r_{0}^{2}}},{H_{a} = \frac{S_{a}}{r_{0}^{2}}},{H_{0} = \frac{S_{0}}{r_{0}^{2}}}} & (43)\end{matrix}$ where; r₀: a diameter of propeller S_(C): an area obtainedby converting the area of stabilizing wing inside of the spreadingpropeller wind into the area of stabilizing wing inside of the shrunkpropeller wind, when the spreading propeller wind is shrunk such thatthe propeller wind flows as a parallel wind flow without changing theair density directly under propeller, but its calculation of shrinkingrate is as follows. Suppose the horizontal line on the stabilizing winglocated at any distance from the propeller, and let the width ofspreading of the propeller wind on its horizontal line be r_(W), thewidth of the stabilizing wing inside of the propeller wind be r_(a), andalso the width of the stabilizing wing on its horizontal line aftershrinking be r, then r is represented by formula (4) $\begin{matrix}{r = {r_{a}\left( \frac{r_{0}}{r_{w}} \right)}^{2}} & (4)\end{matrix}$ S_(a): the area of stabilizing wing inside of exceedingpart of shrunk propeller wind when the area of stabilizing wing insideof the exceeding propeller wind from inside of said spreading propellerwind is shrunk at the shrinking rate represented by formula (4) S₀: thearea (except the area where propeller wind is flowing) of stabilizingwing of propeller periphery. S_(W): the projection area of the wholeaircraft.
 3. The flying object described in claim 1, and wherein furtherformula (28) holds. $\begin{matrix}{{{\pi {\sum\limits_{i}\; {H_{Ci}n_{GCi}}}} + {\underset{j}{\pi\sum}\; {H_{aj}n_{Gaj}}} + {\frac{1}{\pi}{\sum\limits_{m}\; {H_{0m}n_{G\; 0m}}}} + {\frac{\lbrack W\rbrack}{S_{W}}{\sum\limits_{k}\; {S_{Wk}n_{GWk}}}}} \geq n_{G}} & (28)\end{matrix}$ Providing that: $\begin{matrix}{\lbrack W\rbrack = \frac{S_{W}}{\left\lbrack S_{C} \right\rbrack}} & (25) \\{\left\lbrack S_{C} \right\rbrack = {S_{C} + S_{a} + {\frac{1}{\pi^{2}}S_{0}}}} & (23) \\{{H_{Ci} = \frac{S_{Ci}}{r_{0}^{2}}},{H_{aj} = \frac{S_{aj}}{r_{o}^{2}}},{H_{om} = \frac{S_{om}}{r_{0}^{2}}}} & (44)\end{matrix}$ where; r₀: a diameter of propeller S_(C): an area obtainedby converting the area of stabilizing wing inside of the spreadingpropeller wind into the area of stabilizing wing inside of the shrunkpropeller wind, when the spreading propeller wind is shrunk such thatthe propeller wind flows as a parallel wind flow without changing theair density directly under propeller, but its calculation of shrinkingrate is as follows. Suppose the horizontal line on the stabilizing winglocated at any distance from the propeller, and let the width ofspreading of the propeller wind on its horizontal line be r_(W), thewidth of the stabilizing wing inside of the propeller wind be r_(a), andalso the width of the stabilizing wing on its horizontal line aftershrinking be r, then r is represented by formula (3) $\begin{matrix}{r = {r_{a}\left( \frac{r_{0}}{r_{w}} \right)}} & (3)\end{matrix}$ S_(a): the area of stabilizing wing inside of exceedingpart of shrunk propeller wind when the area of stabilizing wing insideof the exceeding propeller wind from inside of said spreading propellerwind is shrunk at the shrinking rate represented by formula (3) S₀: thearea (except the area where propeller wind is flowing) of stabilizingwing of propeller periphery. S_(W): the projection area of the entireaircraft. S_(Ci): the area of each minute part of said S_(C). S_(aj):the area of each minute part of said S_(a) S_(0m): the area of eachminute part of said S₀ S_(Wk); the area of each minute part of saidS_(W) n_(G): the multiple coefficient of the vertical distance betweenthe fixed point of the rotational axis of propeller and the center ofgravity of the aircraft for the diameter of propeller r₀. n_(GCi): themultiple coefficient of the vertical distance between each minute partthat has the area of said S_(Ci) and the center of gravity of theaircraft for the diameter of propeller r₀. n_(Gaj): the multiplecoefficient of the vertical distance between each minute part that hasthe area of said S_(aj) and the center of gravity of the aircraft forthe diameter of propeller r₀. n_(G0m): the multiple coefficient of thevertical distance between each minute part that has the area of saidS_(0m) and the center of gravity of the aircraft for the diameter ofpropeller r₀. n_(GW)k: the multiple coefficient of the vertical distancebetween each minute part that has the area of said S_(Wk) and the centerof gravity of the aircraft for the diameter of propeller r₀.
 4. A flyingobject described in claim 2, and wherein further formula (29) holds.$\begin{matrix}{{{\sum\limits_{i}\; {H_{Ci}n_{GCi}}} + {\sum\limits_{j}\; {H_{aj}n_{Gaj}}} + {\frac{1}{\pi}{\sum\limits_{m}\; {H_{0m}n_{G\; 0m}}}} + {\frac{\lbrack W\rbrack}{S_{W}}{\sum\limits_{k}\; {S_{Wk}n_{GWk}}}}} \geq n_{G}} & (29)\end{matrix}$ Providing that: $\begin{matrix}{\lbrack W\rbrack = \frac{S_{W}}{\left\lbrack S_{C} \right\rbrack}} & (25) \\{\left\lbrack S_{C} \right\rbrack = {S_{C} + S_{a} + {\frac{1}{\pi}S_{0}}}} & (24) \\{{H_{Ci} = \frac{S_{Ci}}{r_{0}^{2}}},{H_{aj} = \frac{S_{aj}}{r_{o}^{2}}},{H_{om} = \frac{S_{om}}{r_{0}^{2}}}} & (44)\end{matrix}$ where r₀: a diameter of propeller S_(C): an area obtainedby converting the area of stabilizing wing inside of the spreadingpropeller wind into the area of stabilizing wing inside of the shrunkpropeller wind, when the spreading propeller wind is shrunk such thatthe propeller wind flows as a parallel wind flow without changing theair density directly under propeller, but its calculation of shrinkingrate is as follows. Suppose the horizontal line on the stabilizing winglocated at any distance from the propeller, and let the width ofspreading of the propeller wind on its horizontal line be r_(W), thewidth of the stabilizing wing inside of the propeller wind be r_(a), andalso the width of the stabilizing wing on its horizontal line aftershrinking be r, then r is represented by formula (4) $\begin{matrix}{r = {r_{a}\left( \frac{r_{0}}{r_{w}} \right)}^{2}} & (4)\end{matrix}$ S_(a): the area of stabilizing wing inside of exceedingpart of shrunk propeller wind when the area of stabilizing wing insideof the exceeding propeller wind from inside of said spreading propellerwind is shrunk at the shrinking rate represented by formula (4). S₀: thearea (except the area where propeller wind is flowing) of stabilizingwing of propeller periphery. S_(W): the projection area of the wholeaircraft. S_(Ci): the area of each minute part of said S_(C). S_(aj):the area of each minute part of said S_(a) S_(0m): the area of eachminute part of said S₀ S_(Wk): the area of each minute part of saidS_(W) n_(G): the multiple coefficient of the vertical distance betweenthe fixed point of the rotational axis of propeller and the center ofgravity of the aircraft for the diameter of propeller r₀. n_(GCi): themultiple coefficient of the vertical distance between each minute partthat has the area of said S_(Ci) and the center of gravity of theaircraft for the diameter of propeller r₀. n_(Gaj): the multiplecoefficient of the vertical distance between each minute part that hasthe area of said S_(aj) and the center of gravity of the aircraft forthe diameter of propeller r₀. n_(G0m): the multiple coefficient of thevertical distance between each minute part that has the area of saidS_(Wk) and the center of gravity of the aircraft for the diameter ofpropeller r₀. n_(GWK): the multiple coefficient of the vertical distancebetween each minute part that has the area of said S_(Wk) and the centerof gravity of the aircraft for the diameter of propeller r₀.
 5. A flyingobject, comprising a wind flow generating device; and one or morecylindrical stabilizing wings arranged along the center line of the windflow in the shape of coaxial line in the wind flow generated byconcerned wind flow generating device, wherein said cylindricalstabilizing wings are arranged such that the relationship between thevertical distance n_(GC) between the center point of total wind flowpressure obtained by synthesizing the center point of wind flow pressureof the respective stabilizing wings and the center of gravity ofconcerned aircraft, and the vertical distance n_(GW) from the centerpoint of outside wind pressure and the center of gravity of the flyingobject, is represented by formula (26).[H]n_(GC)=[W]n_(GW)   (26) Providing that $\begin{matrix}{\lbrack H\rbrack = {\frac{\pi^{2}}{2}H_{D}}} & (32) \\{\lbrack W\rbrack = \frac{S_{W}}{\left\lbrack S_{C} \right\rbrack}} & (25) \\{\left\lbrack S_{C} \right\rbrack = {\frac{\pi}{2}S_{D}}} & (33) \\{H_{D} = \frac{S_{D}}{r_{0}^{2}}} & (37)\end{matrix}$ where; r₀: a diameter of propeller S_(D): the projectionarea of inside wall when inside diameter of cylindrical stabilizing wingis shrunk into the diameter of the propeller. S_(W): the projection areaof the whole aircraft.
 6. The flying object described in claim 5,wherein further formula (34) holds. $\begin{matrix}{{{\frac{\pi^{2}}{2}{\sum\limits_{q}\; {H_{Dq}n_{GDq}}}} + {\frac{\lbrack W\rbrack}{S_{W}}{\sum\limits_{k}\; {S_{Wk}n_{GWk}}}}} \geq n_{G}} & (34)\end{matrix}$ Providing that: $\begin{matrix}{\lbrack W\rbrack = \frac{S_{W}}{\left\lbrack S_{C} \right\rbrack}} & (25) \\{\left\lbrack S_{C} \right\rbrack = {\frac{\pi}{2}S_{D}}} & (33) \\{H_{Dq} = \frac{S_{Dq}}{r_{o}^{2}}} & (39)\end{matrix}$ where; r₀: a diameter of propeller S_(W): the projectionarea of the whole aircraft. S_(D): the projection area of inside wallwhen inside diameter of cylindrical stabilizing wing is shrunk into thediameter of the propeller. S_(Wk): the area of each minute part of saidS_(W) S_(Dq): the are of each minute part of said S_(D) n_(G): themultiple coefficient of the vertical distance between the fixed point ofthe rotational axis of propeller and the center of gravity of theaircraft for the diameter of propeller r₀. n_(GW)k: the multiplecoefficient of the vertical distance between each minute part that hasthe area of said S_(Wk) and the center of gravity of the aircraft forthe diameter of propeller r₀ m_(GDq): the multiple coefficient of thevertical distance between each minute part that has the area of saidS_(Dq) and the center of gravity of the aircraft for the diameter ofpropeller r₀.
 7. A flying object comprising the flying object describedin any one of claims 1 to 4 and the flying object described in claim 5or 6, wherein the respective wind flow generating devices share one windflow generating device.
 8. A flying object, comprising two or more ofthe same flying objects described in any one of claims 1 to 7, which arearranged at intervals with center axes thereof being parallel to eachother and each has an upwardly directed intake and a downwardly directedexhaust; and a connecting member connecting said two or more of the sameflying objects to each other.